An accelerated discrete velocity method for flows of rarefied ternary gas mixtures in long rectangular channels

An accelerated discrete velocity method is presented for rarefied three-component gas mixtures flowing through long rectangular ducts. The scheme is developed on the basis of the McCormack linearized kinetic model. Diffusion equations are derived for the velocity and the heat flow vector. The kinetic and diffusion equations are solved in a coupled iteration. Simulations are carried out for He-Ar-Xe mixture to test the computational performance of the scheme for pressure driven flow. It is shown that the accelerated method requires a fewer number of iterations and smaller computational time in a large part of the gas rarefaction from the transition region to the hydrodynamic limit than the non-accelerated one. These quantities are studied as a function of the convergence parameter also. The flow rates as a function of the rarefaction parameter and representative velocity profiles are shown. A good agreement is found between the total flow rate and the corresponding slip flow value at large rarefaction parameters. The present approach can be useful for fast computation of flows of ternary gas mixtures in long rectangular channels.